A Fast and Efficient Cross-Validation Method for Smoothing Parameter Choice in Spline Regression

Abstract

The spline smoothing approach to nonparametric regression is considered, with particular reference to the problem of choosing how much to smooth. Both computational and statistical aspects of the method of cross-validation are discussed. An approximate cross-validation method is proposed that requires a small linear amount of computer time. A simulation study indicates that the method has very good statistical properties. Some mathematical justification and motivation are also provided.

Key Words:

• Nonparametric regression
• Automatic smoothing
• Splines
• Density estimates